Plotting arbitrary constants in mathematica

[kraigandrews]

How do you plot arbitrary constants in mathematica? for example r(psi)=a(1-eCos(psi)), where a and e are some constant.

Thanks in advance for the help.

 

[Dale]

Well, you cannot plot a function with arbitrary constants. Where would the computer draw the line? However, what you can do is do a Plot inside a Manipulate, like this:

Manipulate[Plot[a (1 - e Cos[psi]), {psi, -1, 1}], {{a, 1}, -2, 2}, {{e, 1}, -2, 2}]

 

[kraigandrews]

OK thanks.

 

[Simon_Tyler]

Some constants can be absorbed into variables by defining dimensionless variables.
This basically treats the constant as the "natural scale" for that dimension.

In your example, you can define the dimensionless, s = r/a
But e is dimensionless and can't really be absorbed anywhere.

So

Manipulate[ Plot[ 1 - e Cos[psi], {psi, -1, 1}, AxesLabel->{"psi","s=r/a"}], {{e,1}, -2, 2}]

 

[alphy]

To plot arbitrary constants in Mathematica, you can use the Plot function and specify the values of the constants a and e in the formula. For example, using the formula r(psi) = a(1-eCos(psi)), you can plot the function for different values of a and e by using the following code:

Plot[a*(1 - e*Cos[psi]), {psi, 0, 2*Pi}, PlotRange -> All]

This will generate a plot of the function with the specified values of a and e. You can also use the Manipulate function to create an interactive plot where you can adjust the values of a and e using sliders. For example:

Manipulate[Plot[a*(1 - e*Cos[psi]), {psi, 0, 2*Pi}, PlotRange -> All], {a, 1, 10}, {e, 0, 1}]

This will create a plot where you can adjust the values of a and e and see the resulting changes in the plot. You can also use the Show function to combine multiple plots with different values of a and e into one plot for comparison. For more complex functions involving arbitrary constants, you may need to use the ParametricPlot function. Overall, Mathematica offers a variety of tools and functions for plotting arbitrary constants and visualizing mathematical equations.